CuBIC  Cumulant Based Inference of higherorder Correlation¶
CuBIC is a statistical method for the detection of higher order of correlations in parallel spike trains based on the analysis of the cumulants of the population count. Given a list sts of SpikeTrains, the analysis comprises the following steps:
 compute the population histogram (PSTH) with the desired bin size
>>> binsize = 5 * pq.ms >>> pop_count = elephant.statistics.time_histogram(sts, binsize)
 apply CuBIC to the population count
>>> alpha = 0.05 # significance level of the tests used >>> xi, p_val, k = cubic(data, ximax=100, alpha=0.05, errorval=4.):

elephant.cubic.
cubic
(data, ximax=100, alpha=0.05)[source]¶ Performs the CuBIC analysis [1] on a population histogram, calculated from a population of spiking neurons.
The null hypothesis is iteratively tested with increasing correlation order (correspondent to variable xi) until it is possible to accept, with a significance level alpha, that (corresponding to variable xi_hat) is the minimum order of correlation necessary to explain the third cumulant .
is the maximized third cumulant, supposing a Compund Poisson Process (CPP) model for correlated spike trains (see [1]) with maximum order of correlation equal to .
Parameters:  data : neo.AnalogSignal
The population histogram (count of spikes per time bin) of the entire population of neurons.
 ximax : int
The maximum number of iteration of the hypothesis test: if it is not possible to compute the before ximax iteration the CuBIC procedure is aborted. Default: 100
 alpha : float
The significance level of the hypothesis tests perfomed. Default: 0.05
Returns:  xi_hat : int
The minimum correlation order estimated by CuBIC, necessary to explain the value of the third cumulant calculated from the population.
 p : list
The ordred list of all the pvalues of the hypothesis tests that have been performed. If the maximum number of iteration ximax is reached the last pvalue is set to 4
 kappa : list
The list of the first three cumulants of the data.
 test_aborted : bool
Wheter the test was aborted because reached the maximum number of iteration ximax
References
[1]Staude, Rotter, Gruen, (2009) J. Comp. Neurosci